The name Thickstone is one of those problematic New Netherland names -- it's spelled in diverse ways in the original records, and the problem is confounded by the fact that authors of published books have imposed one preferred spelling on all the ancestors. Nice work digging up the sources you found, then finding his wife's profile!
The profile for Rachel Hanse-5 has a record for her marriage to Jeremy Fiksten and another record for the baptism of a child with Jeremy Fikston, so your proposed connection is appropriate. All of these names need to be documented in the profiles.
However, I note that the baptism record you found is for the baptism of Jermias Dikston -- that means that Dikston (not Thickstone) should be the LNAB on his profile.
I've not found any other profiles for Jermias/Jeremias/Jeremy, but I've not yet searched to see if we have anything for his parents.
Edited to strike inaccurate statements.